# Why should I use a 1-sample t-test?

To perform this test, select Stat > Basic Statistics > 1-Sample t.

Use the 1-sample t-test to estimate the mean of a population and compare it to a target or reference value when you do not know the standard deviation of the population. Using this test, you can:
• Determine whether the mean of a group differs from a specified value.
• Calculate a range of values that is likely to include the population mean.

For example, the manager of a pizza business collects a random sample of pizza delivery times. The manager uses the 1-sample t-test to determine whether the mean delivery time is significantly lower than a competitor's advertised delivery time of 30 minutes.

The test calculates the difference between your sample mean and the hypothesized mean relative to the variability of your sample. Usually, the larger the difference and the smaller the variability in your sample, the greater the chance that the population mean differs significantly from the hypothesized mean.

The 1-sample t-test also works well when the assumption of normality is violated, but only if the underlying distribution is symmetric, unimodal, and continuous. If the values are highly skewed, it might be appropriate to use a nonparametric procedure, such as a 1-sample sign test.

For 1-Sample t, the hypotheses are:
Null hypothesis
 H0: μ = µ0 The population mean (μ) equals the hypothesized mean (µ0).
Alternative hypothesis
Choose one:
 H1: μ ≠ µ0 The population mean (μ) differs from the hypothesized mean (µ0). H1: μ > µ0 The population mean (μ) is greater than the hypothesized mean (µ0). H1: μ < µ0 The population mean (μ) is less than the hypothesized mean (µ0).
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